Question

Calculate the compound interest
Principal= Rs. 5000
Rate = 5% p.a (compounded annually)
Time= 2 years

Answer 1

Given

• Principal = Rs. 5000
• Rate = 5% p.a
• Time= 2 years

Explanation

As We know that:-

$\maltese {\large{\pmb{\boxed{\sf{ Amount = P \left( 1 + \dfrac{r}{100} \right)^n }}}}}$

We can apply this method to find the Amount of the transaction and then after we can easily derive the Compound Interest of the transaction as:-

$\colon\implies{\sf{ Amount = 5000 \left( 1 + \dfrac{5}{100} \right)^2 }} \\ \\ \\ \colon\implies{\sf{ Amount = 5000 \left( \dfrac{105}{100} \right)^2 }} \\ \\ \\ \colon\implies{\sf{ Amount = 5000 \left( \dfrac{21}{20} \right)^2 }} \\ \\ \\ \colon\implies{\sf{ Amount = 50 \cancel{00} \times \dfrac{21}{2 \cancel{0} } \times \dfrac{21}{2 \cancel{0} } }} \\ \\ \\ \colon\implies{\sf{ Amount = 50 \times \dfrac{21}{2} \times \dfrac{21}{2} }} \\ \\ \\ \colon\implies{\sf{ Amount = \cancel{ \dfrac{22050}{4} } }} \\ \\ \\ \colon\implies{\sf\purple{ Amount = Rs. \ 5512.5 }}$

The Amount of the transaction is ₹5512.5

We also Know that:-

${\pmb{\boxed{\sf\green{ Amount = Principal + Interest }}}} \\ \\ \colon\implies{\sf{ Amount - Principal = Interest }} \\ \\ \colon\implies{\sf{ 5512.5 - 5000 = Interest }} \\ \\ \colon\implies{\sf{ Interest = Rs. \ 512.5 }}$

Hence,

${\underline{\sf{ The \ Compound \ Interest \ of \ the \ transaction \ will \ be \ Rs. \ 512.5 }}}$